Finite Group Databasebeta

← #20243724

Subgroups — #20243724

Order 6016.

402 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic47C211yesmaximal, characteristic
2C2×#13093948C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic
4#15689030C211yesmaximal, characteristic, complemented
5#15688886C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C22×SD16×C47C211yesmaximal, characteristic
8C23×Dic47—21no—
9C22×C47⋊C8C2211yescharacteristic
10D4×Dic47—22no—
11D4×Dic47—22no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C22⋊Dic47—21no—
15C2×C4×Dic47C2211yescharacteristic
16#13093948—22no—
17#13093945—22no—
18C47⋊#95—21no—
19C47⋊#95—21no—
20C22×Q8×C47C2211yescharacteristic
21C22×D4×C47C2211yescharacteristic
22C2×SD16×C47—22no—
23C2×SD16×C47—22no—
24C2×SD16×C47C414yescomplemented
25C22×C8×C47C2211yescharacteristic
26C24×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47C2×C412yescomplemented
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47—21no—
36C2×D4×C47C2×C412yes—
37C2×D4×C47D412yes—
38C2×D4×C47D412yes—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—24no—
42C22×Dic47—21no—
43C22×Dic47—21no—
44C22×Dic47—42no—
45C22×Dic47—42no—
46C22×Dic47D411yescharacteristic
47C22×Dic47D411yescharacteristic
48SD16×C47—28no—
49C2×C8×C47—21no—
50C2×C8×C47—21no—
51C2×C8×C47C2×C412yescomplemented
52C22⋊Dic47—24no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47D412yes—
57C4×Dic47—21no—
58C4×Dic47—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—21no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47—41no—
68C23×C47—41no—
69C23×C47C2×D411yescharacteristic
70Q8×C47—22no—
71Q8×C47—22no—
72Q8×C47—41no—
73Q8×C47—41no—
74D4×C47—22no—
75D4×C47—22no—
76D4×C47—22no—
77D4×C47C22⋊C414yes—
78C2×C4×C47—22no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47C22×C411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47#4111yescharacteristic
86C2×C4×C47#4111yescharacteristic
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—48no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96C2×Dic47—41no—
97C2×Dic47—41no—
98C2×Dic47—41no—
99C2×Dic47SD1612yescomplemented
100C8×C47—22no—
101C47⋊C8—41no—
102C22×C47—24no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47C4×D411yescharacteristic
110C22×C47#12011yescharacteristic
111C22×C47#12111yescharacteristic
112C22×C47C2×SD1611yescharacteristic
113C22×C47#13511yescharacteristic
114C22×C47AGL(1,ℤ/8)11yescharacteristic
115C22×C47#13711yescharacteristic
116C4×C47—42no—
117C4×C47C2×C22⋊C411yescharacteristic
118C4×C47C4×D411yescharacteristic
119C4×C47#12111yescharacteristic
120C4×C47#12311yescharacteristic
121Dic47—22no—
122Dic47—42no—
123Dic47—41no—
124Dic47—81no—
125#1877—471nomaximal, Sylow
126C2×C47—44no—
127C2×C47#38611yescharacteristic
128C2×C47C4×SD1611yescharacteristic
129C2×C47#44011yescharacteristic
130C2×C47#45011yescharacteristic
131C2×C47#45211yescharacteristic
132C2×C47#46111yescharacteristic
133C2×C47#46311yescharacteristic
134C22×SD16D4711yescharacteristic
135C2×C4×D4—471no—
136C2×#103—471no—
137C2×#102—471no—
138#391—471no—
139#340—471no—
140#336—471no—
141C47#187711yescharacteristic, complemented, Sylow
142C22×Q8C2×D4711yescharacteristic
143C22×D4C2×D4711yescharacteristic
144C23×C4—941no—
145C2×SD16—22no—
146C2×SD16—22no—
147C2×SD16Dic4714yescomplemented
148C22×C8—471no—
149C22×C8C2×D4711yescharacteristic
150C4×D4—942no—
151C4×D4—942no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—471no—
154C2×C22⋊C4—941no—
155C2×C42—471no—
156#103—942no—
157#102—942no—
158#95—941no—
159#95—941no—
160C24—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8C2×Dic4712yescomplemented
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4C2×Dic4712yes—
171C2×D4C22⋊D4712yes—
172C2×D4C22⋊D4712yes—
173C22×C4—21no—
174C22×C4—471no—
175C22×C4—471no—
176C22×C4—944no—
177C22×C4—941no—
178C22×C4—941no—
179C22×C4—1882no—
180C22×C4—1882no—
181C22×C4C22×D4711yescharacteristic
182SD16—28no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—941no—
186C2×C8—941no—
187C2×C8—941no—
188C2×C8C2×Dic4712yescomplemented
189C4⋊C4—472no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C22⋊C4—944no—
194C42—941no—
195C42—941no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23D4×D4711yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—41no—
207Q8—41no—
208D4—22no—
209D4—22no—
210D4—22no—
211D4C22⋊Dic4714yes—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—472no—
216C2×C4—941no—
217C2×C4—941no—
218C2×C4—941no—
219C2×C4—942no—
220C2×C4—941no—
221C2×C4—941no—
222C2×C4—1888no—
223C2×C4—1881no—
224C2×C4—1881no—
225C2×C4—1881no—
226C2×C4—1881no—
227C2×C4—1881no—
228C2×C4D4×D4711yescharacteristic
229C2×C4#1062535211yescharacteristic
230C2×C4#1062535211yescharacteristic
231C2×C4C22×Dic4711yescharacteristic
232C2×C4C2×C22⋊D4711yescharacteristic
233C2×C4C2×C22⋊D4711yescharacteristic
234C8—22no—
235C8—1881no—
236C22—24no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22D4×Dic4711yescharacteristic
244C22#1309399211yescharacteristic
245C22#1309399611yescharacteristic
246C22SD16×D4711yescharacteristic
247C22#1309404511yescharacteristic
248C22#1309405111yescharacteristic
249C22#1309405311yescharacteristic
250C4—42no—
251C4—942no—
252C4—3761no—
253C4—1882no—
254C4—1881no—
255C4C2×C22⋊Dic4711yescharacteristic
256C4D4×Dic4711yescharacteristic
257C4#1309399611yescharacteristic
258C4#1309400511yescharacteristic
259C2—44no—
260C2#1568900311yescharacteristic
261C2SD16×Dic4711yescharacteristic
262C2#1568922411yescharacteristic
263C2#1568927211yescharacteristic
264C2#1568928211yescharacteristic
265C2#1568932611yescharacteristic
266C2#1568934011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×SD16×C47C2
socleC23×C47C2×D4
hypercenterC22×SD16D47
hypocenterC47#1877
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#13093948C2semidirect
4. #15689030C2semidirect
5. #15688886C2semidirect
6. #15688877C2semidirect
24. C2×SD16×C47C4semidirect
32. C2×Q8×C47C2×C4semidirect
51. C2×C8×C47C2×C4semidirect
99. C2×Dic47SD16semidirect
141. C47#1877semidirect
147. C2×SD16Dic47semidirect
166. C2×Q8C2×Dic47semidirect
188. C2×C8C2×Dic47semidirect